Identifying an angle

Match these angles with their measures. There should be one angle in each category. We have 30 degrees, 60 degrees, 90 degrees, and 180 degrees. So there's a few that are very easy to spot out. This angle right over here, it makes a complete line. So this is clearly 180 degrees. So this one's 180 degrees. The other one that might jump out at you is this one right over here. This is clearly a right angle, or a 90-degree angle right over here. So this is 90 degrees. And so we have to think which of these is 30 and which is 60 degrees? Well, just by comparing it that way, you know that the one that opens out more is going to be 60 degrees and the one that opens out less is going to be 30 degrees. And you can see that this, the opening here, is half the size of the opening right over here. So it makes sense that this is 30, this is 60, and it also makes sense that this angle is 1/3 the measure of this angle right over here, that this is 90 degrees. And then if you were to double this, then this part of the angle would go all the way out, and you would get to the 180 degrees. So let's check our answer and make sure we actually got this one right. Let's do one more, just for fun. Which of these angles has a measure of 60 degrees? So there's a couple that we can immediately rule out. This angle here is clearly more than 90 degrees. It's an obtuse angle. This angle here is 180 degrees, so we're going to have to pick between these two. And we can assume that these are all at scale. So if we know that a right angle would have this line straight up and down, this looks like it's 2/3 of the way there. So I would go with this one right over there. Now, you might say, well, what about this one? Well, this one looks like it's about 1/3 of a right angle. If we were to do 2/3, then 3/3, it looks like we would get to a right angle. So this one looks much closer to 30 degrees. So which of these angles has a measure of 60? That one right over there. You could immediately rule out that one and that one, and then these take a little bit closer inspection.